Sides and volume of object not rendered through glass
This partially looks like a Z-Fighting problem. 

Try scaling up your Milk Mesh to where its perimeter edges are in the middle of the glass' inner and outer walls and try again.

To do this:


Select your Milk Mesh.
S.
Shift + Z
Move your mouse until it is lined up >> LMB.




Also, if this is still not working altogether after that: 




Select your Milk Mesh.
Go into edit mode (TAB to toggle). 
A to select all.
Ctrl + N to recalculate the normals. 

Go back into Object mode (TAB to toggle). 



Now try rendering again. If it is still not working then hopefully we can get you to post your .blend file



After taking a look at your blend file, here is what I did to get the following results:




1. I applied your Boolean Modifier.



2. I did the scaling step listed above.


3. I modified your glass material to that shown in the result image.


4. I added a Sun Lamp with a Strength of 5.0 (Using Nodes).